46 ideas
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
19917 | Without reason and human help, human life is misery [Spinoza] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
19922 | People are only free if they are guided entirely by reason [Spinoza] |
19935 | Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza] |
19914 | In nature everything has an absolute right to do anything it is capable of doing [Spinoza] |
19915 | Natural rights are determined by desire and power, not by reason [Spinoza] |
7487 | Society exists to extend human awareness [Spinoza, by Watson] |
19943 | The state aims to allow personal development, so its main purpose is freedom [Spinoza] |
19930 | Sovereignty must include the power to make people submit to it [Spinoza] |
19936 | Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza] |
19937 | Monarchs are always proud, and can't back down [Spinoza] |
19940 | Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza] |
19931 | Every state is more frightened of its own citizens than of external enemies [Spinoza] |
19920 | Democracy is a legitimate gathering of people who do whatever they can do [Spinoza] |
19938 | Allowing religious ministers any control of the state is bad for both parties [Spinoza] |
19933 | If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza] |
19923 | Slavery is not just obedience, but acting only in the interests of the master [Spinoza] |
19939 | Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza] |
19944 | Without liberty of thought there is no trust in the state, and corruption follows [Spinoza] |
19942 | Treason may be committed as much by words as by deeds [Spinoza] |
19924 | The freest state is a rational one, where people can submit themselves to reason [Spinoza] |
7827 | Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza] |
19926 | The sovereignty has absolute power over citizens [Spinoza] |
19928 | No one, in giving up their power and right, ceases to be a human being [Spinoza] |
19918 | Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza] |
19919 | People only give up their rights, and keep promises, if they hope for some greater good [Spinoza] |
19921 | Once you have given up your rights, there is no going back [Spinoza] |
19925 | In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza] |
19929 | Everyone who gives up their rights must fear the recipients of them [Spinoza] |
19932 | The early Hebrews, following Moses, gave up their rights to God alone [Spinoza] |
19916 | The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza] |
19927 | State and religious law can clash, so the state must make decisions about religion [Spinoza] |
19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |